Frames for spaces of Paley-Wiener functions on Riemannian manifolds
Abstract
It is shown that Paley-Wiener functions on Riemannian manifolds of bounded geometry can be reconstructed in a stable way from some countable sets of their inner products with certain distributions of compact support. A reconstruction method in terms of frames is given which is a generalization of the classical result of Duffin-Schaeffer about exponential frames on intervals. All results are specified in the case of the two-dimensional hyperbolic space in its Poincare upper half-plane realization.
- Publication:
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arXiv e-prints
- Pub Date:
- April 2011
- DOI:
- 10.48550/arXiv.1104.1710
- arXiv:
- arXiv:1104.1710
- Bibcode:
- 2011arXiv1104.1710P
- Keywords:
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- Mathematics - Functional Analysis;
- Mathematics - Spectral Theory
- E-Print:
- Integral geometry and tomography, 135-148, Contemp. Math., 405, Amer. Math. Soc., Providence, RI, 2006